Following closely to [1]}'s
approach, let \(g(\ x)=\frac{\mu }{2\left(2-\theta \right)}\ \left(1+\left\Vert x\right\Vert ^{2}\right)^{1-\frac{\theta }{2}}\) 
for \(0\le \theta <1\) . The gradient of \(g\left(x\right)\)  is \(\nabla g(\ x)=\frac{\mu }{2}\left(1+\left\Vert x\right\Vert ^{2}\right)^{-\frac{\theta }{2}}x\) 
and the Hessian of \(g\left(x\right)\)  is
\(\nabla ^{2}g(\ x) & =\frac{\mu }{2}\left[\left(1+\left\Vert x\right\Vert ^{2}\right)^{-\frac{\theta }{2}}I_{d}-\theta \left(1+\left\Vert x\right\Vert ^{2}\right)^{-\frac{\theta }{2}-1}xx^{T}\right]\nonumber \\& \preceq \frac{\mu }{2}\left(1+\left\Vert x\right\Vert ^{2}\right)^{-\frac{\theta }{2}}I_{d}.\) 
